ON THE DYNAMICS IN SPACE OF RODS UNDERGOING LARGE MOTIONS - A GEOMETRICALLY EXACT APPROACH

The dynamics of a fully nonlinear rod model, capable of undergoing finite bending, shearing, and extension, is considered in detail. Unlike traditional nonlinear structural dynamics formulations, due to the effect of finite rotations the deformation map takes values in R**3 multiplied by SO(3), which is a differentiable manifold and not a linear space. An implicit time stepping algorithm that furnishes a canonical extension of the classical Newmark algorithm to the rotation group (SO(3)) is developed. In addition to second-order accuracy, the proposed algorithm reduces exactly to the plane formulation. Moreover, the exact linearization of the algorithm and associated configuration update is obtained in closed form, leading to a configuration-dependent nonsymmetric tangent inertia matrix.